Simplify the following expression: $ r = \dfrac{-1}{7} + \dfrac{-9}{10n + 4} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10n + 4}{10n + 4}$ $ \dfrac{-1}{7} \times \dfrac{10n + 4}{10n + 4} = \dfrac{-10n - 4}{70n + 28} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{-9}{10n + 4} \times \dfrac{7}{7} = \dfrac{-63}{70n + 28} $ Therefore $ r = \dfrac{-10n - 4}{70n + 28} + \dfrac{-63}{70n + 28} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-10n - 4 - 63}{70n + 28} $ $r = \dfrac{-10n - 67}{70n + 28}$